In: Resources 03 Mar 2017 Tags: , , , , , ,

The Antenna Factor

By Ron Hranac, Senior Technology Editor

In the world of electromagnetic compatibility (EMC) and electromagnetic interference (EMI) testing, a parameter known as “antenna factor” commonly is used. Antenna factor is not widely known in the cable industry, although it is built in to the calculations used for signal leakage measurements as the “0.021” and “f” (frequency) in the microvolts per meter-to-dBmV conversion formula. ( For more on the mathematics of field-strength measurements, see my June 2008 column at

Wikipedia defines antenna factor as “the ratio of the incident electromagnetic field strength to the voltage V (units: V or µV) on the line connection of an antenna. For an electric field antenna, field strength is in units of V/m or µV/m, and the resulting antenna factor AF is in units of 1/m: AF = E/V.

“The antenna factor for a given antenna is related closely to the load impedance Z0 connected to the antenna’s terminals.”

In other words, antenna factor is the ratio of the field strength of an electromagnetic field incident upon an antenna to the voltage produced by that field across a load of impedance Z0 connected to an antenna’s terminals. (Subsequent references to “antenna terminals” in this article assume those terminals are connected to a suitable load of the desired impedance Z 0).

The field strength can be calculated by multiplying the voltage at the antenna’s terminals by the antenna factor. Many prefer to work in the world of logarithms and decibels, and antenna factor commonly is expressed in decibel format rather than the previously discussed linear format. When antenna factor is stated in decibels, field strength in decibel-microvolts per meter (dBµV/m) is calculated by adding the signal level at the antenna terminals in decibel-microvolts (dBµV) to the antenna factor in decibel/meter (dB/m).

“Whoa!” you say. “We measure signal level in dBmV, not dBµV; and field strength in microvolts per meter (µV/m) rather than dBµV/m.” That’s true in North America, but much of the rest of the world uses dBµV and dBµV/m. Fortunately, it’s not that difficult to convert between dBµV and dBmV, or between dBµV/m and µV/m.

To convert a value in dBµV to dBmV, simply subtract 60 from the dBµV value. Going the other direction, adding 60 to a value in dBmV gives dBµV. For example, +117 dBµV is +57 dBmV, and 0 dBmV is +60 dBµV. Our familiar 20 µV/m signal leakage field strength limit is converted to dBuV/m using the formula:

20log10(value in µV/m)

20log10(20 µV/m)

20 * [log10(20)]

20 * [1.301]

26.02 dBµV/m

Converting from dBµV/m to µV/m is done with the formula µV/m = 10 (value in dBµV/m divided by 20).

Consider a signal-leakage measurement made at 121.2625 MHz (CEA Channel 14’s visual carrier) using a resonant half-wave dipole. We can calculate the antenna factor for that dipole knowing the field strength and the signal level at the antenna terminals.

For instance, assume that the field strength produced by a leak is the previously mentioned 20 µV/m. ( Note: When making a field strength measurement for the purpose of determining antenna factor, ensure that the measurement is in the far field as opposed to the near field; the antenna has been aligned to the same polarity as the electromagnetic field being measured; and that the antenna has been oriented to produce the maximum level at its terminals.) The signal level in dBmV at the antenna’s terminals is found with the formula:

dBmV = 20log10[(E/0.021f)/1000]

where E is the field strength in µV/m and f is the frequency in megahertz.

dBmV=20log10[(20/0.021 * 121.2625)/1000]

= 20log10[(20/2.5465)/1000]

= 20log10[7.8539/1000]

= 20log10[0.0079]

= 20 * [log10(0.0079)]

= 20 * [-2.1049]

= -42.1 dBmV

Now, add 60 to -42.1 dBmV to get the level in dBµV: +17.9 dBµV. We already know that 20 µV/m equals 26.02 dBµV/m, so the antenna factor of our dipole is 26.02 dBµV/m – 17.9 dBµV = 8.12 dB/m. This antenna-factor value applies to this particular antenna at this frequency.

If we make a field-strength measurement at another frequency, the antenna factor will be different than what was just calculated for 121.2625 MHz. For example, if a leak produces a 20 µV/m field strength at 782 MHz, and we measure that field strength with a resonant half-wave dipole for the higher frequency, the level at the antenna’s terminals will be -58.29 dBmV, or +1.71 dBµV. Knowing that 20 µV/m equals 26.02 dBµV/m, the antenna factor is 26.02 dBµV/m – 1.71 dBµV = 24.31 dB/m.

A couple of interesting things become apparent. First, the leakage field strength is 20 µV/m for both frequencies, yet the levels at the two antennas’ terminals are quite different: -42.1 dBmV at 121.2625 MHz versus -58.29 dBmV at 782 MHz. The difference is 16.19 dB, which happens to be equal to the difference between the two antenna factors: 24.31 dB/m – 8.12 dB/m = 16.19 dB.

You’ve probably seen tables or charts that show resonant half-wave dipole antenna levels in dBmV versus frequency for a given signal-leakage field strength. For instance, 20 µV/m field strength produces dipole levels of -42.1 dBmV on Channel 14 (121.2625 MHz), -42.5 dBmV on Channel 15 (127.2625 MHz), -42.9 dBmV on Channel 16 (133.2625 MHz), -43.3 dBmV on Channel 17 (139.25 MHz) and so forth. The reason for the variation in the level at the antenna terminals versus frequency is because of the difference in antenna factor at different frequencies.

So far, I’ve been talking about measurements made using Z0 = 75 ohms impedance equipment (a dipole in free space has an impedance of approximately 73 ohms). EMC and EMI measurements usually are done using Z0 = 50 ohms impedance equipment, making antenna factor slightly different. Half-wave dipole antenna factor in 50 ohms impedance is calculated easily with the formula:

AF50? = 20log10(f) – 10log10(G) – 29.7707


AF50? is the antenna factor for a half-wave dipole connected to a load of Z0 = 50 ohms, f is frequency in megahertz and G is the dipole’s numeric gain (1.64). 10log10(1.64) gives a dipole’s gain in decibels, or 2.15 dBi. For the earlier examples of 121.2625 MHz and 782 MHz, a Z0 = 50 ohms impedance scenario’s half-wave dipole antenna factors are 9.76 dB/m and 25.95 dB/m, respectively.

I’ve not seen a similar antenna factor formula for Z0 = 75 ohms impedance, but it’s easy to sort out. I came up with the following, using Z0 = 73 ohms, a dipole’s approximate free-space impedance:

AF73? = 20log10(f) – 10log10(G) – 31.4142


AF73? is the approximate antenna factor for a half-wave dipole, f is frequency in megahertz, and G is the dipole’s numerical gain (1.64). This formula agrees closely with the earlier calculation, where an antenna factor of 8.12 dB/m was sorted out for 121.2625 MHz. Here it works out to 8.11 dB/m. If Z0 = 75 ohms is used, the formula changes very slightly to:

AF75? = 20log10(f) – 10log10(G) – 31.5315

As you can see, antenna factor for a given antenna is related closely to the load impedance Z0 connected to the antenna’s terminals. In a real-world field-strength measurement, a dipole antenna will be connected to an instrument like a spectrum analyzer via a length of coaxial cable. There might be a bandpass filter or preamplifier in-line, too. One must account for the insertion loss of the coax and such devices as filters (or gain, in the case of a preamplifier) to come up with what the signal level would be at the antenna’s terminals with the load directly connected to the antenna.

But back to the load impedance Z0: A spectrum analyzer might have an input return loss of around 20 dB with input attenuation switched in (it will be lower with the input attenuator set to 0 dB). That 20 dB return loss equates to a voltage standing wave ratio (VSWR) of 1.22:1, which means the actual load impedance Z0 “seen” by the antenna’s terminals could be anywhere in the 61.36 ohms-91.67 ohms range (I’m leaving reactance out of the impedance discussion as well as the contribution of the coax to keep things simple). Using these two extremes of possible load Z0, the calculated antenna factors for a half-wave dipole at 121.2625 MHz work out to 8.8663 dB/m (Z0 = 61.36 ohms) and 7.1229 dB/m (Z0 = 91.67 ohms).

If an unknown field strength at 121.2625 MHz produces a level at a dipole’s terminals of 17.9 dBµV (-42.1 dBmV), we get a range of possible field strengths of 17.9 dBµV + 7.1229 dB/m = 25.02 dBµV/m to 17.9 dBµV + 8.8663 dB/m = 26.77 dBµV/m. In our more familiar microvolts per meter, these values are 17.8 µV/m and 21.8 µV/m, respectively.

In practice, commercial antennas used for EMC/EMI purposes include antenna factor-versus-frequency data provided by the manufacturer.


About the author:

Ron Hranac is technical leader, broadband network engineering at Cisco Systems and senior technology editor for Communications Technology. Contact him at

Article published with the permission of the author.


In: Products, Resources 16 Jun 2014 Tags: , , , ,

To create the Standard-RM propagation model that is faithful to Fresnel’s theory (for frequencies > 30 MHz), it took more than 20 years of research and development and more than 50 iterations of implementation in our software, which has been verified with hundreds of thousands of measurements.

Standard-RM includes the Fresnel complex integral, diffraction (2D and 3D), Ducting, Troposcattering, Climate, Reflections, Refraction, Scattering…


Since 1988, we there have been many different methods for calculating diffraction that we have implemented in our software (Epstein Peterson, Bullington and Deygout). All these methods have one thing in common: they do not take into account the effects of multiple paths that sum together at a given point at a given frequency.  This aspect can be accounted for in various ways as in the following models:

  • Propagation curves CCIR/ITU (370, 1546) with the notion of effective height
  • Okumura-Hata with the notion of effective height
  • Wojnar or Deygout (94) with FPL (fourth-power law)
  • Durkin (with the slope factor corrections altering the fundamental model)
  • Two-ray plane earth models
  • Longley Rice (ITM)
  • Delta-Bullington
  • Etc.


Recommendation ITU-R P.526-13 offers a method of calculating diffraction “sub-path”, inspired by our different models. In this model, the Fresnel integral treated approximately so it is incomplete, however, it demonstrates that when calculating propagation deterministically, that the Fresnel model is important.


2014 ATDI integrates its model RM-Standard in its software ICS and HTZ.

The version released yet incorporates so far FPL + Deygout diffraction, and we only use this to determine the minimum attenuation. Once we have finished checking the new model with measurements, it will become redundant.


This model is entirely dependent on the input data: model quality and accuracy of emission and reception parameters. We noticed that unlike most models which are more “permissive”, an approximate antenna pattern greatly reduces the correlation. In addition, its sensitivity to the accuracy of terrain data requires new cartographic data, including the need to calculate attenuation due to vegetation with an absorption model.


In conclusion, this model does not give “better” results than another, if it is used with data of moderate quality. It is faithful to the physics of waves. Used with qualified data, we have observed a standard deviation of error <2.5 dB instead of 3.2 / 3.4 dB with previous implementations.



  • End of approximations!
  • A pure model faithful to the geometry of the terrain
  • Allow the true validation of the parameters of a plan



  • Very long computation time
  • Requires an accurate and reliable terrain model
  • Requires the actual station parameters



  • Propagation prediction above 30 MHz
  • A reference model for comparison


Base model:

Fresnel Integrals
Diffraction (GTD, 2D, 3D)
Subpath switching (for compatibility with all the diffraction methods)


Ducting (multi-layers)
Mixed path
Gaz attenuation
Rain attenuation
Slant path
Reflection (2D, 3D)
Clutters and buildings (flat attenuations, dB/km attenuations, mixed diffraction/absorption…)

Outdoor, Outdoor/Indoor, Indoor, 2D 1/2 and 3D terrain models
Coverage calculation, Point to Point and Point to Multi-Points, Path budget
Clutter tuning

Avalaible in ICS telecom, ICS designer, ICS LT and HTZ



The Standard-RM model will soon be released (both formulas and method). Check for further announcements on our website


In: Products, Resources 28 Jan 2014 Tags: , , , ,

Every week month, ATDI compares different propagation models for a given service based on very accurate measurements.


This week, FM: Model-Episode 1


Standard deviation

Average error

Correlation factor

Differences < 6 dB

ITU-R 525 Deygout 94 Fine integration

3.42 dB

0.84 dB



ITU-R 1546-5 (Broadcast analog) 50% time 50% locations

7.43 dB

-5.56 dB



ITU-R 1812-3  50% time 50% locations

3.62 dB

1.57 dB



Okumura-Hata / original

5.10 dB

1.38 dB



ITM / NTIA – 50% time 50% locations

6.26 dB

2.12 dB




Next month, Wimax rel 2 (3 600 MHz)



Parameters influencing the correlation:

The configuration of the propagation model: reference (dBd, dBi, dBv), percentage of time and percentage of locations (if applicable), options like Tropo, Climate, Reflections…,

The quality of the cartography used by the planning tool: the resolution of the DTM, and the quality of the clutter file need to be adapted to the technology simulated. Applying the Lee criteria (see below) is for instance a good way to check the sampling resolution to use depending on the frequency of the technology simulated (step = 40 ?),

The quality of the GPS coordinates needs to taken into account: GPS have today an absolute planimetric accuracy of 7.8 meters at a 95% confidence level, and this quality decreases in obstructed environment (decrease of the GDOP)

The fast fading effect and RF prediction: the LEE criteria

One of the main aspects to take also into consideration for the correlation with measurement is the fast fading effect. Lee’s goal was to find a valid method of estimating the local average power of a signal in the mobile radio environment. His conclusion, that the proper technique is to average 50 samples taken over a distance of 40 ? (wavelengths), has become a standard technique, widely used within the industry .This basis have
become so widely accepted that it can sometimes used in situations where Lee sampling is not strictly applicable. Even though it may not be optimum in all situations, it does provide a base-line that allows measurements to be compared.

Background to signal level variations: the envelope of a received mobile radio signal is composed of a slow fading signal with a fast fading signal superimposed on it. In many applications it is necessary to measure the local average power of the slow fading signal by smoothing out (or averaging) the fast fading part.

The fading experienced by a moving receiver has two major causes:

• The multi-path phenomenon: the signal transmitted from the base station is usually blocked by these surrounding structures and many reflected waves are generated. Summing ail of the multi-path waves at the mobile unit results in fast variations in the received signal which is called multi-path fading. It is also called short-term fading or fast fading referring to the short time period during which signals change.

• The variation of the average signal power as the mobile moves. This is due to different propagation paths between the base station and the mobile unit moving over different terrain configurations at different times. Since the propagation path is always changing as the mobile moves, the path loss values and hence local average power of the received signal vary. Because it is affected by the location of the mobile moving in real time and it varies slowly, it is called the local mean of the long term fading.

Since the received mobile radio signal contains both short term and long-term fading, to estimate the local mean of long-term fading that predictable using a planning tool, the fast fading effect has to eliminated from the measured signal, otherwise the true average power and the measured average power will not be the same.

Obtaining a Local Average Signal Power (Local Mean): how to measure the local mean of the signal when the signal is received by a moving receiver, Lee addressed two major questions. His approach to both was aimed at reducing the errors in the measurements:

• The first question is how to choose a proper length of signal data for averaging.

• The second question, after determining the length, is how many independent sample points are needed for averaging over that length.

Choosing the Proper Length of a Local Mean: as we know, the length of a local signal has to be chosen properly. If it is chosen too short, the short-term fading is still present after the averaging process. If it is chosen too long, information about the long-term fading which we want to preserve, will be smoothed out. To find the proper length, Lee calculated the variance of the estimated local mean as a function of the length. It is important to note that he assumed that the fast fading followed Rayleigh statistics. The variance of a set of samples is the square of the standard deviation of the samples from their mean and is a measure of the spread of the sample values. Lee presents a graph of the variance in dB against the length.

This graph guides the choice of the length by showing how much variance we can expect when using different lengths. This choice a matter of judgment rather than hard fact. Lee suggested the choice of:

• Length = 20 ?, if we are willing to accept a 1 ?m spread in a range of 1.6 dB

• Length = 40 ? if we are willing to accept a 1 ?m spread in a range of 1.0 dB.

If we try to choose less than 20 wavelengths, the 1 ?m spread increases quickly. If we try to choose the length 2L greater than 40 ?, the 1?m spread decreases very slowly, but, averaging over longer than 40 wavelengths risks smoothing out of long-term fading information. Lee concluded that a length of between 20 wavelengths and 40 wavelengths is the proper length for averaging the signal. It is proper in the sense that a length significantly shorter or longer is likely to result in a reduced accuracy of measurement.
Sampling Average: when using an analogue filter as an averaging process, it is difficult to control the bandwidth and Lee chose to use arithmetic averaging of samples instead of analogue averaging. This led him to address the question of how many samples should be taken across the length. Lee aimed to minimize the number of samples and calculated how many points were needed. The calculation is based upon taking the average of two
variables with different statistical distributions. Lee calculates how many samples must be used for the resulting average to be within +/- 1 dB of the true mean.

The resulting figure of 50 samples does not guarantee that the average is within +/- 1 dB of the true mean, though it gives a 90% confidence that it will be.

Effects of different fading environments: Lee concluded that the measured length of a signal necessary to obtain the local average power is in the range of 20 to 40 wavelengths (?), based on the Rayleigh distribution. The sufficient number of samples for estimating this local average power values is 50, based on a 90 percent confidence interval and less than 1 dB in error in the estimate. The processed average data retain the long-term fading information which is the local average power of the signal and predictable by a planning tool, while the short-term fading can be considered as filtered.


• Estimate of Local Average Power of a Mobile Radio Signal, William c.y. Lee, IEEE Trans.
Veh.Tech. Vol VT-34, No. l, Feb 1985.
• The Mobile Radio Propagation Channel, David Parsons, John Wiley 8: Sons 1992,
• Valid RF Field Measurements using Lee Sampling criteria, Willteck White paper
• TETRA field measurement protocol, Emmanuel Grenier, ATDI, Feb 2004